A bicycle lock has a four-digit code. The possible digits, 0 What is the probability that the lock code will begin with
through 9, cannot be repeated.
the number 5?
What is the probability that the lock code will not
contain the number 0?

0.1-0.6

Step-by-step explanation:

First let's find the number of the elements in the sample space, that is the total number of codes that can be produced.

The first digit is any of {0, 1, 2...,9}, that is 10 possibilities

the second digit is any of the remaining 9, after having picked one. 

and so on...

so in total there are 10*9*8*7 = 5040 codes.

a. What is the probability that the lock code will begin with 5?

Lets fix the first number as 5. Then there are 9 possibilities for the second digit, 8 for the third on and 7 for the last digit.

Thus, there are 1*9*8*7=504 codes which start with 5.

so 

P(first digit is five)=

b. What is the probability that the lock code will not contain the number 0? 

from the set {0, 1, 2, } we exclude 0, and we are left with {1, 2, ...9}

from which we can form in total 9*8*7*6 codes which do not contain 0.

P(codes without 0)=n(codes without 0)/n(all codes)=(9*8*7*6)/(10*9*8*7)=6/10=0.6

0.1 ; 0.6

15 units use socratic

step-by-step explanation: 15 units

1.0

step-by-step explanation: